id string | subject string | topic string | subtopic string | difficulty string | difficulty_labeling_method string | question_type string | question string | options dict | correct_answer string | correct_answer_value string | solution string | option_explanations dict | concepts_required list | reasoning_steps int64 | answer_type string | language string | origin string | generator string | generator_template_id string | verification_status string | verification_note string | difficulty_note string | source_type string | answer_validation string |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
openstem_001568 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^8 (2x² +0x +4) dx. | {
"A": "280",
"B": "371.33333",
"C": "746.66667",
"D": "373.33333"
} | D | 373.33333 | An antiderivative is (2/3)x³+(0/2)x²+(4)x. Evaluating between 0 and 8 gives (2/3)(8)³+(0/2)(8)²+(4)(8)=373.33333. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 373.33333, not 280.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 373.33333, not 371.33333.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 373.33333, not 7... | [
"definite integration",
"power rule",
"limits of integration"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_integral_poly | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002470 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[4, 7], [1, 3]]. | {
"A": "5",
"B": "3.75",
"C": "2",
"D": "2.5"
} | A | 5 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (4)(3)−(7)(1)=5. | {
"A": "Correct. The worked calculation gives 5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5, not 3.75.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5, not 2.",
"D": "Incorrect. Substituting the stated values into the governing rel... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005004 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 5 Ω and 2 Ω are connected in series; this combination is connected in parallel with a 2 Ω resistor across a 18 V ideal battery. Find the total current supplied by the battery. | {
"A": "23.14286 A",
"B": "13.57143 A",
"C": "11.57143 A",
"D": "17.35714 A"
} | C | 11.57143 A | Series branch resistance=5+2=7 Ω. Parallel equivalent R_eq=(7×2)/(7+2)=1.55556 Ω. Total current I=V/R_eq=18/1.55556=11.57143 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 11.57143 A, not 23.14286 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 11.57143 A, not 13.57143 A.",
"C": "Correct. The worked calculation gives 11.57143 A.",
"D": "Incorrect. Substitutin... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000998 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 4 and common ratio 5. What is the sum of its first 9 terms? | {
"A": "1953124",
"B": "2343748.8",
"C": "3906248",
"D": "1953126"
} | A | 1953124 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=4(5^9−1)/(5−1)=1953124. | {
"A": "Correct. The worked calculation gives 1953124.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1953124, not 2343748.8.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1953124, not 3906248.",
"D": "Incorrect. Substituting the stated ... | [
"geometric progression",
"finite geometric sum"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_gp_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004089 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 41 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.43. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "104.96 N",
"B": "-104.96 N",
"C": "78.72 N",
"D": "125.952 N"
} | A | 104.96 N | Net force=mg(sinθ−μcosθ)=41×10×(0.6−0.43×0.8)=104.96 N. | {
"A": "Correct. The worked calculation gives 104.96 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 104.96 N, not -104.96 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 104.96 N, not 78.72 N.",
"D": "Incorrect. Substituting the stat... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004646 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 4 kg and radius 6 m is acted on by a constant torque of 57 N m about its central axis. Find its angular acceleration. | {
"A": "1.1875 rad s⁻²",
"B": "0.79167 rad s⁻²",
"C": "-1.20833 rad s⁻²",
"D": "3.79167 rad s⁻²"
} | B | 0.79167 rad s⁻² | For a solid disc, I=½MR²=½(4)(6)²=72 kg m². Using τ=Iα, α=57/72=0.79167 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.79167 rad s⁻², not 1.1875 rad s⁻².",
"B": "Correct. The worked calculation gives 0.79167 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.79167 rad s⁻², not -1.20833 rad s⁻².",
"D"... | [
"moment of inertia",
"rotational dynamics",
"torque"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_disc_torque | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006665 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 2 kg is attached to an ideal spring of force constant 750 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.10328 s",
"B": "0.07746 s",
"C": "3.10328 s",
"D": "0.15492 s"
} | A | 0.10328 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(2/750)=0.10328 s. | {
"A": "Correct. The worked calculation gives 0.10328 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.10328 s, not 0.07746 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.10328 s, not 3.10328 s.",
"D": "Incorrect. Substituting the... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008882 | chemistry | physical_chemistry | equilibrium_degree_dissociation | very_hard | provisional_template_level_label | single_correct_mcq | For A(g) ⇌ 2B(g), the initial concentration of A is 1.47 mol L⁻¹ and initially B is absent. At equilibrium, 28% of A has dissociated at constant volume. Find K_c. | {
"A": "3.64027",
"B": "1.64027",
"C": "0.64027",
"D": "-2.35973"
} | C | 0.64027 | Let α=0.28. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.47)(0.28)²/(1−0.28)=0.64027. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.64027, not 3.64027.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.64027, not 1.64027.",
"C": "Correct. The worked calculation gives 0.64027.",
"D": "Incorrect. Substituting the stated va... | [
"chemical equilibrium",
"equilibrium constant",
"degree of dissociation"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_equilibrium_alpha | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004528 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 2 kg and radius 5 m is acted on by a constant torque of 9 N m about its central axis. Find its angular acceleration. | {
"A": "3.36 rad s⁻²",
"B": "0.36 rad s⁻²",
"C": "0.18 rad s⁻²",
"D": "-0.36 rad s⁻²"
} | B | 0.36 rad s⁻² | For a solid disc, I=½MR²=½(2)(5)²=25 kg m². Using τ=Iα, α=9/25=0.36 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.36 rad s⁻², not 3.36 rad s⁻².",
"B": "Correct. The worked calculation gives 0.36 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.36 rad s⁻², not 0.18 rad s⁻².",
"D": "Incorrect. S... | [
"moment of inertia",
"rotational dynamics",
"torque"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_disc_torque | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006606 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 15 kg is attached to an ideal spring of force constant 201 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.27318 s",
"B": "1.05464 s",
"C": "1.09272 s",
"D": "0.54636 s"
} | D | 0.54636 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(15/201)=0.54636 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.54636 s, not 0.27318 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.54636 s, not 1.05464 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.54636 s,... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006868 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 29 mol H₂ and 8 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "17 mol",
"B": "2.6 mol",
"C": "12 mol",
"D": "16 mol"
} | D | 16 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 29 mol H₂O; O₂ can produce 16 mol H₂O. The limiting condition is O₂; product=16 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 16 mol, not 17 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 16 mol, not 2.6 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 16 mol, not 12 mol.",... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002153 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 3 red, 6 blue and 6 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.31429",
"B": "3.31429",
"C": "2.31429",
"D": "0.62857"
} | A | 0.31429 | Favourable pairs = C(3,2)+C(6,2)+C(6,2)=33. Total pairs=C(15,2)=105. Therefore P=33/105=0.31429. | {
"A": "Correct. The worked calculation gives 0.31429.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.31429, not 3.31429.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.31429, not 2.31429.",
"D": "Incorrect. Substituting the stated va... | [
"classical probability",
"combinations",
"without replacement"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_probability_colours | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005503 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 72 μF capacitor is charged to a potential difference of 30 V. Calculate the energy stored, expressed in μJ. | {
"A": "32400 μJ",
"B": "3241 μJ",
"C": "24300 μJ",
"D": "16200 μJ"
} | A | 32400 μJ | U=½CV². Since C=72 μF, U in μJ is ½×72×(30)²=32400 μJ. | {
"A": "Correct. The worked calculation gives 32400 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 32400 μJ, not 3241 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 32400 μJ, not 24300 μJ.",
"D": "Incorrect. Substituting the state... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003399 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 47 m s⁻¹ at 18° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "129.84176 m",
"B": "155.81011 m",
"C": "103.87341 m",
"D": "127.84176 m"
} | A | 129.84176 m | Range R=u²sin(2θ)/g. Substituting u=47, θ=18° and g=10 gives R=(47)²sin(36°)/10=129.84176 m. | {
"A": "Correct. The worked calculation gives 129.84176 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 129.84176 m, not 155.81011 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 129.84176 m, not 103.87341 m.",
"D": "Incorrect. Substi... | [
"projectile motion",
"range equation",
"trigonometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_projectile_range | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002205 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 5 red, 10 blue and 12 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "3.34473",
"B": "-1.65527",
"C": "0.34473",
"D": "0.68946"
} | C | 0.34473 | Favourable pairs = C(5,2)+C(10,2)+C(12,2)=121. Total pairs=C(27,2)=351. Therefore P=121/351=0.34473. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.34473, not 3.34473.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.34473, not -1.65527.",
"C": "Correct. The worked calculation gives 0.34473.",
"D": "Incorrect. Substituting the stated v... | [
"classical probability",
"combinations",
"without replacement"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_probability_colours | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001808 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 10 elements can be selected from a set of 15 distinct elements? | {
"A": "3005",
"B": "-3003",
"C": "3003",
"D": "3603.6"
} | C | 3003 | Order does not matter, so the count is C(15,10)=15!/[10!(5)!]=3003. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3003, not 3005.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3003, not -3003.",
"C": "Correct. The worked calculation gives 3003.",
"D": "Incorrect. Substituting the stated values into the ... | [
"combinations",
"factorials"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_combinations | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008313 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 15 A for 12769 s. Assuming 100% current efficiency, calculate the mass of copper deposited. Use M(Cu)=63.5 g mol⁻¹ and F=96500 C mol⁻¹. | {
"A": "75.62159 g",
"B": "63.01799 g",
"C": "65.01799 g",
"D": "62.01799 g"
} | B | 63.01799 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×15×12769/(2×96500)=63.01799 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 63.01799 g, not 75.62159 g.",
"B": "Correct. The worked calculation gives 63.01799 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 63.01799 g, not 65.01799 g.",
"D": "Incorrect. Substitutin... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006297 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 32 cm in front of a thin convex lens of focal length 8 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.5",
"B": "-0.66667",
"C": "0.33333",
"D": "-2.66667"
} | C | 0.33333 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(32)(8)/(32−8)=10.66667 cm. Thus |m|=v/u=10.66667/32=0.33333. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.33333, not 0.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.33333, not -0.66667.",
"C": "Correct. The worked calculation gives 0.33333.",
"D": "Incorrect. Substituting the stated value... | [
"thin lens equation",
"linear magnification",
"real image"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_lens_magnification | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000462 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 28 and common difference 6. Find the sum of its first 15 terms. | {
"A": "1052",
"B": "1048",
"C": "1050",
"D": "525"
} | C | 1050 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=28, d=6, n=15: Sₙ=15/2[2(28)+(15−1)(6)]=1050. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1050, not 1052.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1050, not 1048.",
"C": "Correct. The worked calculation gives 1050.",
"D": "Incorrect. Substituting the stated values into the g... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001258 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-5x³ -5x² -6x+7. Evaluate f′(1). | {
"A": "-24.8",
"B": "-62",
"C": "-31",
"D": "-32"
} | C | -31 | Differentiate: f′(x)=3(-5)x²+2(-5)x+(-6). At x=1, f′(1)=3(-5)(1)²+2(-5)(1)+(-6)=-31. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -31, not -24.8.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -31, not -62.",
"C": "Correct. The worked calculation gives -31.",
"D": "Incorrect. Substituting the stated values into the gove... | [
"power rule",
"polynomial derivative"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_derivative_cubic | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000090 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 7x^2 +18x +5=0, let its roots be α and β. What is α²+β²? | {
"A": "3.88776",
"B": "3.18367",
"C": "5.18367",
"D": "-5.18367"
} | C | 5.18367 | By Vieta's relations, α+β = -18/7 and αβ = 5/7. Then α²+β²=(α+β)²−2αβ = (-18/7)²−2(5/7) = 5.18367. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5.18367, not 3.88776.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5.18367, not 3.18367.",
"C": "Correct. The worked calculation gives 5.18367.",
"D": "Incorrect. Substituting the stated va... | [
"Vieta's formulas",
"symmetric polynomial expressions"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_quadratic_vieta | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008913 | chemistry | physical_chemistry | equilibrium_degree_dissociation | very_hard | provisional_template_level_label | single_correct_mcq | For A(g) ⇌ 2B(g), the initial concentration of A is 0.21 mol L⁻¹ and initially B is absent. At equilibrium, 38% of A has dissociated at constant volume. Find K_c. | {
"A": "3.19564",
"B": "2.19564",
"C": "1.19564",
"D": "0.19564"
} | D | 0.19564 | Let α=0.38. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.21)(0.38)²/(1−0.38)=0.19564. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.19564, not 3.19564.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.19564, not 2.19564.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.19564, not 1.195... | [
"chemical equilibrium",
"equilibrium constant",
"degree of dissociation"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_equilibrium_alpha | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003732 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 12 kg block initially moves at 6 m s⁻¹. A constant net force does 12 N of work over 2 m in the direction of motion. Find its final kinetic energy. | {
"A": "120 J",
"B": "192 J",
"C": "242 J",
"D": "240 J"
} | D | 240 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(12)(6)²+(12)(2)=240 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 240 J, not 120 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 240 J, not 192 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 240 J, not 242 J.",
"D":... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002181 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 8 red, 11 blue and 12 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "-0.67957",
"B": "0.32043",
"C": "1.32043",
"D": "0.16022"
} | B | 0.32043 | Favourable pairs = C(8,2)+C(11,2)+C(12,2)=149. Total pairs=C(31,2)=465. Therefore P=149/465=0.32043. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.32043, not -0.67957.",
"B": "Correct. The worked calculation gives 0.32043.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.32043, not 1.32043.",
"D": "Incorrect. Substituting the stated v... | [
"classical probability",
"combinations",
"without replacement"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_probability_colours | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003691 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 5 kg block initially moves at 11 m s⁻¹. A constant net force does 17 N of work over 3 m in the direction of motion. Find its final kinetic energy. | {
"A": "353.5 J",
"B": "-353.5 J",
"C": "176.75 J",
"D": "355.5 J"
} | A | 353.5 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(5)(11)²+(17)(3)=353.5 J. | {
"A": "Correct. The worked calculation gives 353.5 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 353.5 J, not -353.5 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 353.5 J, not 176.75 J.",
"D": "Incorrect. Substituting the stated ... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007914 | chemistry | physical_chemistry | first_order_half_life | hard | provisional_template_level_label | single_correct_mcq | A first-order reaction has a half-life of 20 minutes. If the initial reactant concentration is 20 mmol L⁻¹, what concentration remains after 140 minutes? | {
"A": "-1.84375 mmol L⁻¹",
"B": "1.15625 mmol L⁻¹",
"C": "3.15625 mmol L⁻¹",
"D": "0.15625 mmol L⁻¹"
} | D | 0.15625 mmol L⁻¹ | 140 minutes corresponds to 7 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=20/2^7=0.15625 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.15625 mmol L⁻¹, not -1.84375 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.15625 mmol L⁻¹, not 1.15625 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the govern... | [
"first-order kinetics",
"half-life",
"exponential decay"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_first_order_halflife | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001818 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 5 elements can be selected from a set of 87 distinct elements? | {
"A": "73899714",
"B": "27712392.75",
"C": "36949859",
"D": "36949857"
} | D | 36949857 | Order does not matter, so the count is C(87,5)=87!/[5!(82)!]=36949857. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 36949857, not 73899714.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 36949857, not 27712392.75.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 36949857, n... | [
"combinations",
"factorials"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_combinations | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008761 | chemistry | physical_chemistry | equilibrium_degree_dissociation | very_hard | provisional_template_level_label | single_correct_mcq | For A(g) ⇌ 2B(g), the initial concentration of A is 0.76 mol L⁻¹ and initially B is absent. At equilibrium, 45% of A has dissociated at constant volume. Find K_c. | {
"A": "0.11927",
"B": "4.11927",
"C": "1.11927",
"D": "1.11193"
} | C | 1.11927 | Let α=0.45. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.76)(0.45)²/(1−0.45)=1.11927. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.11927, not 0.11927.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.11927, not 4.11927.",
"C": "Correct. The worked calculation gives 1.11927.",
"D": "Incorrect. Substituting the stated va... | [
"chemical equilibrium",
"equilibrium constant",
"degree of dissociation"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_equilibrium_alpha | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001599 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^3 (1x² +1x +2) dx. | {
"A": "15.6",
"B": "18.5",
"C": "19.5",
"D": "21.5"
} | C | 19.5 | An antiderivative is (1/3)x³+(1/2)x²+(2)x. Evaluating between 0 and 3 gives (1/3)(3)³+(1/2)(3)²+(2)(3)=19.5. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 19.5, not 15.6.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 19.5, not 18.5.",
"C": "Correct. The worked calculation gives 19.5.",
"D": "Incorrect. Substituting the stated values into the g... | [
"definite integration",
"power rule",
"limits of integration"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_integral_poly | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000265 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 2x^2 -7x +1=0, let its roots be α and β. What is α²+β²? | {
"A": "9.25",
"B": "2.125",
"C": "11.25",
"D": "10.25"
} | C | 11.25 | By Vieta's relations, α+β = 7/2 and αβ = 1/2. Then α²+β²=(α+β)²−2αβ = (7/2)²−2(1/2) = 11.25. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 11.25, not 9.25.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 11.25, not 2.125.",
"C": "Correct. The worked calculation gives 11.25.",
"D": "Incorrect. Substituting the stated values into t... | [
"Vieta's formulas",
"symmetric polynomial expressions"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_quadratic_vieta | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002572 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[3, 3], [3, 8]]. | {
"A": "15",
"B": "22.5",
"C": "11.25",
"D": "12"
} | A | 15 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (3)(8)−(3)(3)=15. | {
"A": "Correct. The worked calculation gives 15.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 15, not 22.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 15, not 11.25.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004004 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 9 kg block initially moves at 11 m s⁻¹. A constant net force does 19 N of work over 9 m in the direction of motion. Find its final kinetic energy. | {
"A": "717.5 J",
"B": "715.5 J",
"C": "716.5 J",
"D": "858.6 J"
} | B | 715.5 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(9)(11)²+(19)(9)=715.5 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 715.5 J, not 717.5 J.",
"B": "Correct. The worked calculation gives 715.5 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 715.5 J, not 716.5 J.",
"D": "Incorrect. Substituting the stated va... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002235 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 3 red, 12 blue and 7 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.38961",
"B": "1.03896",
"C": "-0.38961",
"D": "2.38961"
} | A | 0.38961 | Favourable pairs = C(3,2)+C(12,2)+C(7,2)=90. Total pairs=C(22,2)=231. Therefore P=90/231=0.38961. | {
"A": "Correct. The worked calculation gives 0.38961.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.38961, not 1.03896.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.38961, not -0.38961.",
"D": "Incorrect. Substituting the stated v... | [
"classical probability",
"combinations",
"without replacement"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_probability_colours | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001717 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 5 elements can be selected from a set of 23 distinct elements? | {
"A": "33648",
"B": "3365.9",
"C": "33649",
"D": "16824.5"
} | C | 33649 | Order does not matter, so the count is C(23,5)=23!/[5!(18)!]=33649. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 33649, not 33648.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 33649, not 3365.9.",
"C": "Correct. The worked calculation gives 33649.",
"D": "Incorrect. Substituting the stated values into... | [
"combinations",
"factorials"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_combinations | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007978 | chemistry | physical_chemistry | first_order_half_life | hard | provisional_template_level_label | single_correct_mcq | A first-order reaction has a half-life of 20 minutes. If the initial reactant concentration is 53 mmol L⁻¹, what concentration remains after 100 minutes? | {
"A": "1.65625 mmol L⁻¹",
"B": "1.24219 mmol L⁻¹",
"C": "0.65625 mmol L⁻¹",
"D": "3.3125 mmol L⁻¹"
} | A | 1.65625 mmol L⁻¹ | 100 minutes corresponds to 5 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=53/2^5=1.65625 mmol L⁻¹. | {
"A": "Correct. The worked calculation gives 1.65625 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.65625 mmol L⁻¹, not 1.24219 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.65625 mmol L⁻¹, not 0.65625 mmol L⁻¹.",
... | [
"first-order kinetics",
"half-life",
"exponential decay"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_first_order_halflife | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009392 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_6H_11N_1. Treat X as the total number of monovalent halogen atoms. | {
"A": "0",
"B": "2",
"C": "1",
"D": "4"
} | B | 2 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×6+2+1−11−0)/2=2. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2, not 0.",
"B": "Correct. The worked calculation gives 2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2, not 1.",
"D": "Incorrect. Substituting the stated values into the governing relati... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004039 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 46 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.12. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "347.76 N",
"B": "231.84 N",
"C": "173.88 N",
"D": "463.68 N"
} | B | 231.84 N | Net force=mg(sinθ−μcosθ)=46×10×(0.6−0.12×0.8)=231.84 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 231.84 N, not 347.76 N.",
"B": "Correct. The worked calculation gives 231.84 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 231.84 N, not 173.88 N.",
"D": "Incorrect. Substituting the stat... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008757 | chemistry | physical_chemistry | equilibrium_degree_dissociation | very_hard | provisional_template_level_label | single_correct_mcq | For A(g) ⇌ 2B(g), the initial concentration of A is 0.59 mol L⁻¹ and initially B is absent. At equilibrium, 55% of A has dissociated at constant volume. Find K_c. | {
"A": "3.17289",
"B": "0.79322",
"C": "-1.41356",
"D": "1.58644"
} | D | 1.58644 | Let α=0.55. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.59)(0.55)²/(1−0.55)=1.58644. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.58644, not 3.17289.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.58644, not 0.79322.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.58644, not -1.41... | [
"chemical equilibrium",
"equilibrium constant",
"degree of dissociation"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_equilibrium_alpha | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002413 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[4, 2], [2, 8]]. | {
"A": "56",
"B": "28",
"C": "14",
"D": "27"
} | B | 28 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (4)(8)−(2)(2)=28. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 28, not 56.",
"B": "Correct. The worked calculation gives 28.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 28, not 14.",
"D": "Incorrect. Substituting the stated values into the governing r... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009762 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Pd(OH)_4]^+0, each OH ligand has charge −1. Determine the formal oxidation state of Pd. | {
"A": "-4",
"B": "6",
"C": "5",
"D": "4"
} | D | 4 | Let the formal oxidation state of Pd be x. Charge balance gives x+(4)(−1)=+0; hence x=0+4=+4. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4, not -4.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4, not 6.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4, not 5.",
"D": "Correct. The worked c... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002687 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-2, -3, 1) and v=(0, -5, 7), calculate u·v. | {
"A": "22",
"B": "23",
"C": "33",
"D": "16.5"
} | A | 22 | The dot product is the sum of corresponding component products: (-2)(0)+(-3)(-5)+(1)(7)=22. | {
"A": "Correct. The worked calculation gives 22.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 22, not 23.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 22, not 33.",
"D": "Incorrect. Substituting the stated values into the governing r... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009064 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.84 V, transfers 1 electrons, and has reaction quotient Q=10^-1. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "0.8991 V",
"B": "3.8991 V",
"C": "-1.1009 V",
"D": "2.8991 V"
} | A | 0.8991 V | Apply the Nernst equation: E=0.84−(0.0591/1)(-1)=0.8991 V. | {
"A": "Correct. The worked calculation gives 0.8991 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.8991 V, not 3.8991 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.8991 V, not -1.1009 V.",
"D": "Incorrect. Substituting the sta... | [
"electrochemical cells",
"Nernst equation",
"logarithms"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_nernst | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000226 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 4x^2 +8x -7=0, let its roots be α and β. What is α²+β²? | {
"A": "4.5",
"B": "7.5",
"C": "-7.5",
"D": "9.5"
} | B | 7.5 | By Vieta's relations, α+β = -8/4 and αβ = -7/4. Then α²+β²=(α+β)²−2αβ = (-8/4)²−2(-7/4) = 7.5. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7.5, not 4.5.",
"B": "Correct. The worked calculation gives 7.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 7.5, not -7.5.",
"D": "Incorrect. Substituting the stated values into the gover... | [
"Vieta's formulas",
"symmetric polynomial expressions"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_quadratic_vieta | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004076 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 32 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.16. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "16.104 N",
"B": "75.52 N",
"C": "151.04 N",
"D": "181.248 N"
} | C | 151.04 N | Net force=mg(sinθ−μcosθ)=32×10×(0.6−0.16×0.8)=151.04 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 151.04 N, not 16.104 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 151.04 N, not 75.52 N.",
"C": "Correct. The worked calculation gives 151.04 N.",
"D": "Incorrect. Substituting the state... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003779 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 9 kg block initially moves at 0 m s⁻¹. A constant net force does 22 N of work over 11 m in the direction of motion. Find its final kinetic energy. | {
"A": "242 J",
"B": "-242 J",
"C": "484 J",
"D": "181.5 J"
} | A | 242 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(9)(0)²+(22)(11)=242 J. | {
"A": "Correct. The worked calculation gives 242 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 242 J, not -242 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 242 J, not 484 J.",
"D": "Incorrect. Substituting the stated values into... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007279 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 2 mol of gas at 360 K and 1.21 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "36.62048 L",
"B": "48.82731 L",
"C": "58.59277 L",
"D": "47.82731 L"
} | B | 48.82731 L | PV=nRT, so V=nRT/P=(2)(0.082057)(360)/(1.21)=48.82731 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 48.82731 L, not 36.62048 L.",
"B": "Correct. The worked calculation gives 48.82731 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 48.82731 L, not 58.59277 L.",
"D": "Incorrect. Substitutin... | [
"ideal gas equation",
"unit consistency"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_ideal_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000746 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 9 and common ratio 5. What is the sum of its first 8 terms? | {
"A": "-878904",
"B": "878903",
"C": "87891.4",
"D": "878904"
} | D | 878904 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=9(5^8−1)/(5−1)=878904. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 878904, not -878904.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 878904, not 878903.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 878904, not 87891.4."... | [
"geometric progression",
"finite geometric sum"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_gp_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008635 | chemistry | physical_chemistry | boiling_point_elevation | hard | provisional_template_level_label | single_correct_mcq | A non-volatile solute is dissolved in water to produce a solution of molality 1.19 mol kg⁻¹. If its van't Hoff factor is 1 and K_b for water is 0.52 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "-1.3812 K",
"B": "0.4641 K",
"C": "0.6188 K",
"D": "1.06188 K"
} | C | 0.6188 K | ΔT_b=iK_bm. Substitution gives ΔT_b=1×0.52×1.19=0.6188 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.6188 K, not -1.3812 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.6188 K, not 0.4641 K.",
"C": "Correct. The worked calculation gives 0.6188 K.",
"D": "Incorrect. Substituting the sta... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002938 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(2, 5, 4) and v=(0, 6, 2), calculate u·v. | {
"A": "45.6",
"B": "36",
"C": "19",
"D": "38"
} | D | 38 | The dot product is the sum of corresponding component products: (2)(0)+(5)(6)+(4)(2)=38. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 38, not 45.6.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 38, not 36.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 38, not 19.",
"D": "Correct. The w... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007829 | chemistry | physical_chemistry | first_order_half_life | hard | provisional_template_level_label | single_correct_mcq | A first-order reaction has a half-life of 20 minutes. If the initial reactant concentration is 21 mmol L⁻¹, what concentration remains after 60 minutes? | {
"A": "1.2625 mmol L⁻¹",
"B": "2.625 mmol L⁻¹",
"C": "1.625 mmol L⁻¹",
"D": "-0.375 mmol L⁻¹"
} | B | 2.625 mmol L⁻¹ | 60 minutes corresponds to 3 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=21/2^3=2.625 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.625 mmol L⁻¹, not 1.2625 mmol L⁻¹.",
"B": "Correct. The worked calculation gives 2.625 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.625 mmol L⁻¹, not 1.625 mmol L⁻¹.",
"D": "I... | [
"first-order kinetics",
"half-life",
"exponential decay"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_first_order_halflife | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009385 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_12H_15N_1X_4. Treat X as the total number of monovalent halogen atoms. | {
"A": "5",
"B": "3",
"C": "2",
"D": "4"
} | D | 4 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×12+2+1−15−4)/2=4. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4, not 5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4, not 3.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4, not 2.",
"D": "Correct. The worked ca... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003361 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 37 m s⁻¹ at 55° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "192.96588 m",
"B": "64.32196 m",
"C": "129.64392 m",
"D": "128.64392 m"
} | D | 128.64392 m | Range R=u²sin(2θ)/g. Substituting u=37, θ=55° and g=10 gives R=(37)²sin(110°)/10=128.64392 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 128.64392 m, not 192.96588 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 128.64392 m, not 64.32196 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 128... | [
"projectile motion",
"range equation",
"trigonometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_projectile_range | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008187 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 13 A for 23529 s. Assuming 100% current efficiency, calculate the mass of copper deposited. Use M(Cu)=63.5 g mol⁻¹ and F=96500 C mol⁻¹. | {
"A": "50.31914 g",
"B": "150.95743 g",
"C": "100.63829 g",
"D": "-100.63829 g"
} | C | 100.63829 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×13×23529/(2×96500)=100.63829 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 100.63829 g, not 50.31914 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 100.63829 g, not 150.95743 g.",
"C": "Correct. The worked calculation gives 100.63829 g.",
"D": "Incorrect. Substit... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004095 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 38 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.30. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "205.2 N",
"B": "68.4 N",
"C": "136.8 N",
"D": "14.68 N"
} | C | 136.8 N | Net force=mg(sinθ−μcosθ)=38×10×(0.6−0.30×0.8)=136.8 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 136.8 N, not 205.2 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 136.8 N, not 68.4 N.",
"C": "Correct. The worked calculation gives 136.8 N.",
"D": "Incorrect. Substituting the stated val... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003158 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-2-10i)/(7+2i). What is Re(z), the real part of z? | {
"A": "2.35849",
"B": "0.35849",
"C": "-1.64151",
"D": "-0.64151"
} | D | -0.64151 | Multiply numerator and denominator by the conjugate (7-2i). Then Re(z)=(ac+bd)/(c²+d²)=((-2)(7)+(-10)(2))/(7²+(2)²)=-0.64151. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -0.64151, not 2.35849.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -0.64151, not 0.35849.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -0.64151, not -1... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008090 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 6 A for 908 s. Assuming 100% current efficiency, calculate the mass of copper deposited. Use M(Cu)=63.5 g mol⁻¹ and F=96500 C mol⁻¹. | {
"A": "-1.79248 g",
"B": "1.79248 g",
"C": "0.79248 g",
"D": "1.17925 g"
} | B | 1.79248 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×6×908/(2×96500)=1.79248 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.79248 g, not -1.79248 g.",
"B": "Correct. The worked calculation gives 1.79248 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.79248 g, not 0.79248 g.",
"D": "Incorrect. Substituting th... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005505 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 11 μF capacitor is charged to a potential difference of 22 V. Calculate the energy stored, expressed in μJ. | {
"A": "-2662 μJ",
"B": "2129.6 μJ",
"C": "2663 μJ",
"D": "2662 μJ"
} | D | 2662 μJ | U=½CV². Since C=11 μF, U in μJ is ½×11×(22)²=2662 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2662 μJ, not -2662 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2662 μJ, not 2129.6 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2662 μJ, not 26... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006933 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 32 mol H₂ and 31 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "32 mol",
"B": "24 mol",
"C": "16 mol",
"D": "30 mol"
} | A | 32 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 32 mol H₂O; O₂ can produce 62 mol H₂O. The limiting condition is H₂; product=32 mol. | {
"A": "Correct. The worked calculation gives 32 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 32 mol, not 24 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 32 mol, not 16 mol.",
"D": "Incorrect. Substituting the stated values ... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003270 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(11+9i)/(11+3i). What is Re(z), the real part of z? | {
"A": "-1.86154",
"B": "1.13846",
"C": "0.13846",
"D": "1.11385"
} | B | 1.13846 | Multiply numerator and denominator by the conjugate (11-3i). Then Re(z)=(ac+bd)/(c²+d²)=((11)(11)+(9)(3))/(11²+(3)²)=1.13846. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.13846, not -1.86154.",
"B": "Correct. The worked calculation gives 1.13846.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.13846, not 0.13846.",
"D": "Incorrect. Substituting the stated v... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006511 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 5 kg is attached to an ideal spring of force constant 858 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.11451 s",
"B": "0.15268 s",
"C": "2.15268 s",
"D": "3.15268 s"
} | B | 0.15268 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(5/858)=0.15268 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.15268 s, not 0.11451 s.",
"B": "Correct. The worked calculation gives 0.15268 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.15268 s, not 2.15268 s.",
"D": "Incorrect. Substituting the... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004907 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 15 Ω and 7 Ω are connected in series; this combination is connected in parallel with a 8 Ω resistor across a 24 V ideal battery. Find the total current supplied by the battery. | {
"A": "4.09091 A",
"B": "6.09091 A",
"C": "1.40909 A",
"D": "2.04545 A"
} | A | 4.09091 A | Series branch resistance=15+7=22 Ω. Parallel equivalent R_eq=(22×8)/(22+8)=5.86667 Ω. Total current I=V/R_eq=24/5.86667=4.09091 A. | {
"A": "Correct. The worked calculation gives 4.09091 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4.09091 A, not 6.09091 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4.09091 A, not 1.40909 A.",
"D": "Incorrect. Substituting the... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005359 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 74 μF capacitor is charged to a potential difference of 7 V. Calculate the energy stored, expressed in μJ. | {
"A": "1450.4 μJ",
"B": "3626 μJ",
"C": "1812 μJ",
"D": "1813 μJ"
} | D | 1813 μJ | U=½CV². Since C=74 μF, U in μJ is ½×74×(7)²=1813 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1813 μJ, not 1450.4 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1813 μJ, not 3626 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1813 μJ, not 181... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004406 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 9 kg and radius 3 m is acted on by a constant torque of 89 N m about its central axis. Find its angular acceleration. | {
"A": "5.19753 rad s⁻²",
"B": "3.2963 rad s⁻²",
"C": "2.19753 rad s⁻²",
"D": "3.19753 rad s⁻²"
} | C | 2.19753 rad s⁻² | For a solid disc, I=½MR²=½(9)(3)²=40.5 kg m². Using τ=Iα, α=89/40.5=2.19753 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.19753 rad s⁻², not 5.19753 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.19753 rad s⁻², not 3.2963 rad s⁻².",
"C": "Correct. The worked calculation gives 2.19753 rad s⁻².",
"D":... | [
"moment of inertia",
"rotational dynamics",
"torque"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_disc_torque | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007086 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 18 mol of gas at 542 K and 0.44 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "182.94275 L",
"B": "-1819.42748 L",
"C": "3638.85496 L",
"D": "1819.42748 L"
} | D | 1819.42748 L | PV=nRT, so V=nRT/P=(18)(0.082057)(542)/(0.44)=1819.42748 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1819.42748 L, not 182.94275 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1819.42748 L, not -1819.42748 L.",
"C": "Incorrect. Substituting the stated values into the governing relation give... | [
"ideal gas equation",
"unit consistency"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_ideal_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008921 | chemistry | physical_chemistry | equilibrium_degree_dissociation | very_hard | provisional_template_level_label | single_correct_mcq | For A(g) ⇌ 2B(g), the initial concentration of A is 1.09 mol L⁻¹ and initially B is absent. At equilibrium, 18% of A has dissociated at constant volume. Find K_c. | {
"A": "-2.82773",
"B": "-0.17227",
"C": "0.34455",
"D": "0.17227"
} | D | 0.17227 | Let α=0.18. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.09)(0.18)²/(1−0.18)=0.17227. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.17227, not -2.82773.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.17227, not -0.17227.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.17227, not 0.3... | [
"chemical equilibrium",
"equilibrium constant",
"degree of dissociation"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_equilibrium_alpha | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008042 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 7 A for 19597 s. Assuming 100% current efficiency, calculate the mass of copper deposited. Use M(Cu)=63.5 g mol⁻¹ and F=96500 C mol⁻¹. | {
"A": "44.13402 g",
"B": "67.70103 g",
"C": "45.13402 g",
"D": "54.16083 g"
} | C | 45.13402 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×7×19597/(2×96500)=45.13402 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 45.13402 g, not 44.13402 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 45.13402 g, not 67.70103 g.",
"C": "Correct. The worked calculation gives 45.13402 g.",
"D": "Incorrect. Substitutin... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009859 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Mn(Cl)_6]^+0, each Cl ligand has charge −1. Determine the formal oxidation state of Mn. | {
"A": "8",
"B": "6",
"C": "1.6",
"D": "9"
} | B | 6 | Let the formal oxidation state of Mn be x. Charge balance gives x+(6)(−1)=+0; hence x=0+6=+6. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6, not 8.",
"B": "Correct. The worked calculation gives 6.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6, not 1.6.",
"D": "Incorrect. Substituting the stated values into the governing rela... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000669 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 3 and common ratio 5. What is the sum of its first 11 terms? | {
"A": "18310546.5",
"B": "-36621093",
"C": "43945311.6",
"D": "36621093"
} | D | 36621093 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=3(5^11−1)/(5−1)=36621093. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 36621093, not 18310546.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 36621093, not -36621093.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 36621093, n... | [
"geometric progression",
"finite geometric sum"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_gp_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000465 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 0 and common difference 2. Find the sum of its first 26 terms. | {
"A": "649",
"B": "-650",
"C": "651",
"D": "650"
} | D | 650 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=0, d=2, n=26: Sₙ=26/2[2(0)+(26−1)(2)]=650. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 650, not 649.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 650, not -650.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 650, not 651.",
"D": "Correct. ... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009908 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Pt(Cl)_4]^+2, each Cl ligand has charge −1. Determine the formal oxidation state of Pt. | {
"A": "9",
"B": "6",
"C": "-6",
"D": "3"
} | B | 6 | Let the formal oxidation state of Pt be x. Charge balance gives x+(4)(−1)=+2; hence x=2+4=+6. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6, not 9.",
"B": "Correct. The worked calculation gives 6.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6, not -6.",
"D": "Incorrect. Substituting the stated values into the governing relat... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009244 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.14 V, transfers 3 electrons, and has reaction quotient Q=10^5. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "1.0415 V",
"B": "-1.0415 V",
"C": "0.78112 V",
"D": "3.0415 V"
} | A | 1.0415 V | Apply the Nernst equation: E=1.14−(0.0591/3)(5)=1.0415 V. | {
"A": "Correct. The worked calculation gives 1.0415 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.0415 V, not -1.0415 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.0415 V, not 0.78112 V.",
"D": "Incorrect. Substituting the st... | [
"electrochemical cells",
"Nernst equation",
"logarithms"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_nernst | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009007 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.08 V, transfers 2 electrons, and has reaction quotient Q=10^-2. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "2.1391 V",
"B": "4.1391 V",
"C": "0.85433 V",
"D": "1.1391 V"
} | D | 1.1391 V | Apply the Nernst equation: E=1.08−(0.0591/2)(-2)=1.1391 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.1391 V, not 2.1391 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.1391 V, not 4.1391 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.1391 V, not ... | [
"electrochemical cells",
"Nernst equation",
"logarithms"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_nernst | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005034 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +4 μC and +7 μC are separated by 11 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "20.82645 N",
"B": "18.82645 N",
"C": "22.82645 N",
"D": "16.66116 N"
} | A | 20.82645 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(4×10⁻⁶)(7×10⁻⁶)/(11×10⁻²)²=20.82645 N. | {
"A": "Correct. The worked calculation gives 20.82645 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 20.82645 N, not 18.82645 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 20.82645 N, not 22.82645 N.",
"D": "Incorrect. Substitutin... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009181 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.26 V, transfers 3 electrons, and has reaction quotient Q=10^-3. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "1.3191 V",
"B": "-0.6809 V",
"C": "1.13191 V",
"D": "-1.3191 V"
} | A | 1.3191 V | Apply the Nernst equation: E=1.26−(0.0591/3)(-3)=1.3191 V. | {
"A": "Correct. The worked calculation gives 1.3191 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.3191 V, not -0.6809 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.3191 V, not 1.13191 V.",
"D": "Incorrect. Substituting the st... | [
"electrochemical cells",
"Nernst equation",
"logarithms"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_nernst | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008031 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 14 A for 17837 s. Assuming 100% current efficiency, calculate the mass of copper deposited. Use M(Cu)=63.5 g mol⁻¹ and F=96500 C mol⁻¹. | {
"A": "-82.1611 g",
"B": "82.1611 g",
"C": "41.08055 g",
"D": "65.72888 g"
} | B | 82.1611 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×14×17837/(2×96500)=82.1611 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 82.1611 g, not -82.1611 g.",
"B": "Correct. The worked calculation gives 82.1611 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 82.1611 g, not 41.08055 g.",
"D": "Incorrect. Substituting t... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004438 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 10 kg and radius 1 m is acted on by a constant torque of 57 N m about its central axis. Find its angular acceleration. | {
"A": "2.14 rad s⁻²",
"B": "-11.4 rad s⁻²",
"C": "8.55 rad s⁻²",
"D": "11.4 rad s⁻²"
} | D | 11.4 rad s⁻² | For a solid disc, I=½MR²=½(10)(1)²=5 kg m². Using τ=Iα, α=57/5=11.4 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 11.4 rad s⁻², not 2.14 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 11.4 rad s⁻², not -11.4 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation giv... | [
"moment of inertia",
"rotational dynamics",
"torque"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_disc_torque | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004574 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 5 kg and radius 1 m is acted on by a constant torque of 59 N m about its central axis. Find its angular acceleration. | {
"A": "23.6 rad s⁻²",
"B": "25.6 rad s⁻²",
"C": "22.6 rad s⁻²",
"D": "47.2 rad s⁻²"
} | A | 23.6 rad s⁻² | For a solid disc, I=½MR²=½(5)(1)²=2.5 kg m². Using τ=Iα, α=59/2.5=23.6 rad s⁻². | {
"A": "Correct. The worked calculation gives 23.6 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 23.6 rad s⁻², not 25.6 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 23.6 rad s⁻², not 22.6 rad s⁻².",
"D": "Incorrect. S... | [
"moment of inertia",
"rotational dynamics",
"torque"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_disc_torque | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006329 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 122 cm in front of a thin convex lens of focal length 30 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "1.32609",
"B": "-0.32609",
"C": "3.32609",
"D": "0.32609"
} | D | 0.32609 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(122)(30)/(122−30)=39.78261 cm. Thus |m|=v/u=39.78261/122=0.32609. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.32609, not 1.32609.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.32609, not -0.32609.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.32609, not 3.32... | [
"thin lens equation",
"linear magnification",
"real image"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_lens_magnification | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004688 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 10 Ω and 8 Ω are connected in series; this combination is connected in parallel with a 20 Ω resistor across a 30 V ideal battery. Find the total current supplied by the battery. | {
"A": "1.58333 A",
"B": "0.16667 A",
"C": "2.16667 A",
"D": "3.16667 A"
} | D | 3.16667 A | Series branch resistance=10+8=18 Ω. Parallel equivalent R_eq=(18×20)/(18+20)=9.47368 Ω. Total current I=V/R_eq=30/9.47368=3.16667 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.16667 A, not 1.58333 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.16667 A, not 0.16667 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.16667 A,... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006925 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 9 mol H₂ and 3 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "7 mol",
"B": "8 mol",
"C": "4.5 mol",
"D": "6 mol"
} | D | 6 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 9 mol H₂O; O₂ can produce 6 mol H₂O. The limiting condition is O₂; product=6 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6 mol, not 7 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6 mol, not 8 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6 mol, not 4.5 mol.",
"D... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007752 | chemistry | physical_chemistry | first_order_half_life | hard | provisional_template_level_label | single_correct_mcq | A first-order reaction has a half-life of 20 minutes. If the initial reactant concentration is 47 mmol L⁻¹, what concentration remains after 140 minutes? | {
"A": "0.36719 mmol L⁻¹",
"B": "1.36719 mmol L⁻¹",
"C": "0.73438 mmol L⁻¹",
"D": "0.55078 mmol L⁻¹"
} | A | 0.36719 mmol L⁻¹ | 140 minutes corresponds to 7 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=47/2^7=0.36719 mmol L⁻¹. | {
"A": "Correct. The worked calculation gives 0.36719 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.36719 mmol L⁻¹, not 1.36719 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.36719 mmol L⁻¹, not 0.73438 mmol L⁻¹.",
... | [
"first-order kinetics",
"half-life",
"exponential decay"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_first_order_halflife | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007681 | chemistry | physical_chemistry | first_order_half_life | hard | provisional_template_level_label | single_correct_mcq | A first-order reaction has a half-life of 20 minutes. If the initial reactant concentration is 43 mmol L⁻¹, what concentration remains after 20 minutes? | {
"A": "16.125 mmol L⁻¹",
"B": "22.5 mmol L⁻¹",
"C": "25.8 mmol L⁻¹",
"D": "21.5 mmol L⁻¹"
} | D | 21.5 mmol L⁻¹ | 20 minutes corresponds to 1 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=43/2^1=21.5 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 21.5 mmol L⁻¹, not 16.125 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 21.5 mmol L⁻¹, not 22.5 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relatio... | [
"first-order kinetics",
"half-life",
"exponential decay"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_first_order_halflife | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005920 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 1.7 atm at 365 K. What is its pressure at 652 K? | {
"A": "2.27753 atm",
"B": "3.03671 atm",
"C": "2.03671 atm",
"D": "4.55507 atm"
} | B | 3.03671 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(1.7)(652)/(365)=3.03671 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.03671 atm, not 2.27753 atm.",
"B": "Correct. The worked calculation gives 3.03671 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.03671 atm, not 2.03671 atm.",
"D": "Incorrect. Substi... | [
"ideal gas law",
"isochoric process",
"absolute temperature"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_isochoric_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009708 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Fe(CN)_3]^-1, each CN ligand has charge −1. Determine the formal oxidation state of Fe. | {
"A": "2",
"B": "5",
"C": "1.2",
"D": "3"
} | A | 2 | Let the formal oxidation state of Fe be x. Charge balance gives x+(3)(−1)=-1; hence x=-1+3=+2. | {
"A": "Correct. The worked calculation gives 2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2, not 5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2, not 1.2.",
"D": "Incorrect. Substituting the stated values into the governing rela... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005783 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 3.6 atm at 270 K. What is its pressure at 522 K? | {
"A": "7.96 atm",
"B": "1.696 atm",
"C": "3.48 atm",
"D": "6.96 atm"
} | D | 6.96 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(3.6)(522)/(270)=6.96 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6.96 atm, not 7.96 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6.96 atm, not 1.696 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6.96 atm, not... | [
"ideal gas law",
"isochoric process",
"absolute temperature"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_isochoric_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009086 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.75 V, transfers 2 electrons, and has reaction quotient Q=10^0. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "1.75 V",
"B": "1.075 V",
"C": "0.75 V",
"D": "0.375 V"
} | C | 0.75 V | Apply the Nernst equation: E=0.75−(0.0591/2)(0)=0.75 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.75 V, not 1.75 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.75 V, not 1.075 V.",
"C": "Correct. The worked calculation gives 0.75 V.",
"D": "Incorrect. Substituting the stated values... | [
"electrochemical cells",
"Nernst equation",
"logarithms"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_nernst | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006331 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 75 cm in front of a thin convex lens of focal length 28 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "-2.40426",
"B": "0.89362",
"C": "-0.59574",
"D": "0.59574"
} | D | 0.59574 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(75)(28)/(75−28)=44.68085 cm. Thus |m|=v/u=44.68085/75=0.59574. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.59574, not -2.40426.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.59574, not 0.89362.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.59574, not -0.5... | [
"thin lens equation",
"linear magnification",
"real image"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_lens_magnification | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007256 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 12 mol of gas at 311 K and 2.53 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "90.78164 L",
"B": "121.04218 L",
"C": "13.10422 L",
"D": "120.04218 L"
} | B | 121.04218 L | PV=nRT, so V=nRT/P=(12)(0.082057)(311)/(2.53)=121.04218 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 121.04218 L, not 90.78164 L.",
"B": "Correct. The worked calculation gives 121.04218 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 121.04218 L, not 13.10422 L.",
"D": "Incorrect. Substitu... | [
"ideal gas equation",
"unit consistency"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_ideal_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009036 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.15 V, transfers 2 electrons, and has reaction quotient Q=10^1. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "-1.12045 V",
"B": "2.12045 V",
"C": "0.12045 V",
"D": "1.12045 V"
} | D | 1.12045 V | Apply the Nernst equation: E=1.15−(0.0591/2)(1)=1.12045 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.12045 V, not -1.12045 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.12045 V, not 2.12045 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.12045 V... | [
"electrochemical cells",
"Nernst equation",
"logarithms"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_nernst | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003287 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(4+12i)/(1+6i). What is Re(z), the real part of z? | {
"A": "2.05405",
"B": "1.20541",
"C": "-0.94595",
"D": "3.08108"
} | A | 2.05405 | Multiply numerator and denominator by the conjugate (1-6i). Then Re(z)=(ac+bd)/(c²+d²)=((4)(1)+(12)(6))/(1²+(6)²)=2.05405. | {
"A": "Correct. The worked calculation gives 2.05405.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.05405, not 1.20541.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.05405, not -0.94595.",
"D": "Incorrect. Substituting the stated v... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002849 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(0, 1, 2) and v=(9, 6, 0), calculate u·v. | {
"A": "3",
"B": "1.6",
"C": "9",
"D": "6"
} | D | 6 | The dot product is the sum of corresponding component products: (0)(9)+(1)(6)+(2)(0)=6. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6, not 3.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6, not 1.6.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6, not 9.",
"D": "Correct. The worked ... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008868 | chemistry | physical_chemistry | equilibrium_degree_dissociation | very_hard | provisional_template_level_label | single_correct_mcq | For A(g) ⇌ 2B(g), the initial concentration of A is 1.97 mol L⁻¹ and initially B is absent. At equilibrium, 36% of A has dissociated at constant volume. Find K_c. | {
"A": "3.5957",
"B": "-1.4043",
"C": "1.5957",
"D": "1.15957"
} | C | 1.5957 | Let α=0.36. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.97)(0.36)²/(1−0.36)=1.5957. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.5957, not 3.5957.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.5957, not -1.4043.",
"C": "Correct. The worked calculation gives 1.5957.",
"D": "Incorrect. Substituting the stated values... | [
"chemical equilibrium",
"equilibrium constant",
"degree of dissociation"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_equilibrium_alpha | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001992 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 11 elements can be selected from a set of 37 distinct elements? | {
"A": "854992152",
"B": "1025990582.4",
"C": "854992153",
"D": "854992154"
} | A | 854992152 | Order does not matter, so the count is C(37,11)=37!/[11!(26)!]=854992152. | {
"A": "Correct. The worked calculation gives 854992152.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 854992152, not 1025990582.4.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 854992152, not 854992153.",
"D": "Incorrect. Substituting ... | [
"combinations",
"factorials"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_combinations | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005351 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 70 μF capacitor is charged to a potential difference of 3 V. Calculate the energy stored, expressed in μJ. | {
"A": "-315 μJ",
"B": "315 μJ",
"C": "317 μJ",
"D": "252 μJ"
} | B | 315 μJ | U=½CV². Since C=70 μF, U in μJ is ½×70×(3)²=315 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 315 μJ, not -315 μJ.",
"B": "Correct. The worked calculation gives 315 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 315 μJ, not 317 μJ.",
"D": "Incorrect. Substituting the stated values... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001876 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 5 elements can be selected from a set of 79 distinct elements? | {
"A": "22537516",
"B": "22537515",
"C": "45075030",
"D": "27045018"
} | B | 22537515 | Order does not matter, so the count is C(79,5)=79!/[5!(74)!]=22537515. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 22537515, not 22537516.",
"B": "Correct. The worked calculation gives 22537515.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 22537515, not 45075030.",
"D": "Incorrect. Substituting the stat... | [
"combinations",
"factorials"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_combinations | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008884 | chemistry | physical_chemistry | equilibrium_degree_dissociation | very_hard | provisional_template_level_label | single_correct_mcq | For A(g) ⇌ 2B(g), the initial concentration of A is 1.96 mol L⁻¹ and initially B is absent. At equilibrium, 10% of A has dissociated at constant volume. Find K_c. | {
"A": "0.08711",
"B": "1.00871",
"C": "-2.91289",
"D": "3.08711"
} | A | 0.08711 | Let α=0.1. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.96)(0.1)²/(1−0.1)=0.08711. | {
"A": "Correct. The worked calculation gives 0.08711.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.08711, not 1.00871.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.08711, not -2.91289.",
"D": "Incorrect. Substituting the stated v... | [
"chemical equilibrium",
"equilibrium constant",
"degree of dissociation"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_equilibrium_alpha | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000845 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 4 and common ratio 2. What is the sum of its first 5 terms? | {
"A": "13.4",
"B": "125",
"C": "124",
"D": "122"
} | C | 124 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=4(2^5−1)/(2−1)=124. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 124, not 13.4.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 124, not 125.",
"C": "Correct. The worked calculation gives 124.",
"D": "Incorrect. Substituting the stated values into the gover... | [
"geometric progression",
"finite geometric sum"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_gp_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005289 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +2 μC and +5 μC are separated by 10 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "9 N",
"B": "4.5 N",
"C": "6 N",
"D": "11 N"
} | A | 9 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(2×10⁻⁶)(5×10⁻⁶)/(10×10⁻²)²=9 N. | {
"A": "Correct. The worked calculation gives 9 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 9 N, not 4.5 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 9 N, not 6 N.",
"D": "Incorrect. Substituting the stated values into the gove... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008145 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 5 A for 16897 s. Assuming 100% current efficiency, calculate the mass of copper deposited. Use M(Cu)=63.5 g mol⁻¹ and F=96500 C mol⁻¹. | {
"A": "27.79688 g",
"B": "-27.79688 g",
"C": "13.89844 g",
"D": "28.79688 g"
} | A | 27.79688 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×5×16897/(2×96500)=27.79688 g. | {
"A": "Correct. The worked calculation gives 27.79688 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 27.79688 g, not -27.79688 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 27.79688 g, not 13.89844 g.",
"D": "Incorrect. Substituti... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004215 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 22 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.15. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "105.6 N",
"B": "52.8 N",
"C": "107.6 N",
"D": "-105.6 N"
} | A | 105.6 N | Net force=mg(sinθ−μcosθ)=22×10×(0.6−0.15×0.8)=105.6 N. | {
"A": "Correct. The worked calculation gives 105.6 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 105.6 N, not 52.8 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 105.6 N, not 107.6 N.",
"D": "Incorrect. Substituting the stated val... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
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